The temperature dependence of the site-dependent nuclear spin relaxation time T 1 around vortices is studied in s-wave and d-wave superconductors. Reflecting low-energy electronic excitations associated with the vortex core, temperature dependences deviate from those of the zero-field case, and T 1 becomes faster when approaching the vortex core. In the core region, T 21 1 has a new peak below T c . The NMR study by the resonance field dependence may be a new method to prove the spatial resolved vortex core structure in various superconductors.

Giant negative thermal expansion is achieved in antiperovskite manganese nitrides when the sharp volume change associated with magnetic ordering is broadened by substitution. In this Letter, we address the unique role of the ''magic" element, Ge, for such broadening in Mn3Cu1-xGexN. We present evidence for a local lattice distortion well described by the low-temperature tetragonal (T4) structure of Mn3GeN for a range of x, where the overall structure remains cubic. This structural instability shows a strong correlation with the broadness of the growth of the ordered magnetic moment and, hence, is considered to trigger the broadening of the volume change.

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The temperature and field dependences of the site-selective nuclear spin relaxation time T1 around vortices are studied comparatively both for s-wave and d-wave superconductors, based on the microscopic Bogoliubov-de Gennes theory. Reflecting low energy electronic excitations associated with the vortex core, the site selective temperature dependences deviate from those of the zero-field case, and T1 becomes faster with approaching the vortex core. In the core region, T −1 1 has a new peak below the superconducting transition temperature Tc. The field dependence of the overall T1(T ) behaviors for s-wave and d-wave superconductors is investigated and analyzed in terms of the local density of states. The NMR study by the resonance field dependence may be a new method to probe the spatial resolved vortex core structure in various conventional and unconventional superconductors.

The vortex structure in superconducting stripe states is studied according to the Bogoliubov-de Gennes theory on the two-dimensional Hubbard model with nearest-neighbor sites pairing interaction. The vortex is trapped at the outside region of the stripe line, where the superconductivity is weak. The superconducting coherence length along the stripe direction becomes long. There are no eminent low-energy electronic states even near the vortex core. These characters resemble the Josephson vortex in layered superconductors under a parallel field.KEYWORDS: vortex structure, stripe state, local density of states, Bogoliubov-de Gennes theory Recently, much attention has been focused on the stripe state of underdoped high-T c cuprates. The stripe state was proposed to explain the static magnetic incommensurate structure observed by means of elastic neutron scattering experiments on La 2−x Sr x CuO 4 (LSCO) 1, 2, 3) and La 1.6−x Nd 0.4 Sr x CuO 4 (LNSCO). 4, 5)It is considered that doped holes are localized in the stripe region, which contributes to the one-dimensional (1D) metallic conduction, 6) and the outside region of the stripe is an antiferromagnetic (AF) insulator. Angleresolved photoemission (ARPES) experiments were carried and the 1D-like Fermi surface in the stripe state was observed.7, 8, 9, 10) In YBa 2 Cu 3 O 7−δ , incommensurate fluctuations that were consistent with the above stripe concept were reported by means of inelastic neutron scattering experiments. 11, 12, 13)In high-T c superconductors, it is considered that the low-energy electronic state around the vortex is completely different from that of conventional superconductors. Theoretical studies 14,15,16,17,18) suggest that the low-energy electronic state around the vortex core extends a significant distance due to the line node of the d-wave superconducting gap in high-T c superconductors. Thus, we expect the zero-energy peak in the local density of states (LDOS) at the vortex core, instead of the quantized energy level of the conventional s-wave pairing case. However, in the direct observation of the vortex core by scanning tunneling microscopy (STM), there is no eminent low-energy state around the vortex core. There appears only a small unexplained shoulder or isolated peak at a higher energy within the superconducting gap. 19,20,21,22) These results suggest that we must consider the vortex state, including the exotic character of the electronic state which is unique to high-T c materials. 23,24,25) We study the effect of the stripe state in this paper.Although there are many theoretical approaches to the stripe state, we base this study on the self-consistent Hartree-Fock (HF) theory of the Hubbard model. It is * E-mail address: oka@mp.okayama-u.ac.jp believed that the stripe concept is valid beyond the HF approximation.26) We can consider the metallic stripe state by using the self-consistent HF theory if we consider the realistic Fermi surface topology.27, 28) It can reproduce "the 1D Fermi surface with the gap near ( 7, 8, 9, 10) It also qu...